Thermal–Bioconvective Analysis of Slip-Affected Oldroyd-B Nanofluid Flow Using Artificial Neural Networks

Recent advancements in nanoparticle technology have attracted substantial attention due to their enhanced thermal properties and broad applicability across engineering and thermal sciences. Nanoparticles are widely utilized in energy systems, heating and cooling processes, and material engineering, as well as in biomedical applications such as brain tumor therapy, targeted cell destruction, and cancer treatment. Moreover, the bioconvective behavior of nanoparticles plays a crucial role in various bioscience applications, including biofuel production, enzyme activity, and biosensor design. Motivated by these promising applications, the present study investigates the bioconvective flow of an Oldroyd-B nanofluid in a convectively heated environment using a hybrid Levenberg–Marquardt Backpropagation Neural Network (LMLABPNN) framework. The model incorporates partial slip and thermal effects to accurately capture the underlying flow characteristics. The governing equations are formulated under appropriate physical assumptions and reduced to a system of ordinary differential equations through suitable similarity transformations. The bvp4c solver is then employed to generate high-quality training data for the LMLA-BPNN, enabling reliable prediction of temperature, velocity, and nanoparticle concentration profiles within the bioconvective Oldroyd-B fluid. The performance of the proposed LMLA-BPNN approach is assessed under various parametric conditions and validated against reference numerical solutions. Statistical evaluation techniques—including state transition dynamics, mean square error analysis, regression performance, and error distribution histograms—demonstrate the accuracy, robustness, and reliability of the neural network model in solving the considered physical problem.